OpticsIntro

Concept module

Refraction / Snell's Law

Watch one light ray cross a boundary, connect refractive index to speed change, and see Snell's law set the refracted angle, bending direction, and critical-angle limit on the same live diagram.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Drag the incoming ray or use the sliders. The boundary diagram, critical-angle readouts, and response graphs stay on the same Snell-law model.

Graphs

Switch graph views without breaking the live stage and time link.

Incident to refracted angle

Shows how the transmitted angle changes as you vary the incident angle for the current pair of media.

incident angle theta_1 (°): 0 to 80refracted angle theta_2 (°): 0 to 90

Refracted angle

Hover or scrub to link the graph back to the stage.incident angle theta_1 (°) / refracted angle theta_2 (°)

Controls

Adjust the physical parameters and watch the motion respond.

Incident angle

θ_{1}

50°

Changes the angle between the incoming ray and the normal.

Top-medium index n1

n_{1}

Higher n means slower light in the top medium.

Bottom-medium index n2

n_{2}

1.5

Higher n means slower light in the bottom medium.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Show

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

Graph readingPrompt 1 of 2

Notice that this graph is a family of different boundary setups, not a time trace. Hovering previews a different incident angle immediately.

Try this

Hover farther to the right on the graph and watch the stage jump to the matching incident angle instead of advancing in time.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

θ_{1}

Incident angle

50°

Sets how steeply the incoming ray approaches the normal. Larger incident angles amplify the boundary contrast and can reach the critical-angle limit.

Graph: Incident to refracted angleGraph: Bend relative to the normalOverlay: Normal and angle guideOverlay: Critical-angle guide

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Stay with one boundary at a time. The point is to connect the speed change, the ray direction, and the graph family before you move on.

Graph readingPrompt 1 of 2

Graph: Incident to refracted angle

Notice that this graph is a family of different boundary setups, not a time trace. Hovering previews a different incident angle immediately.

Try this

Hover farther to the right on the graph and watch the stage jump to the matching incident angle instead of advancing in time.

Why it matters

It keeps the graph honest: you are comparing setups at one boundary, not watching a later moment.

Graph: Incident to refracted angle

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

2 visible

Overlay focus

Normal and angle guide

Shows the interface normal and the angle markers for the incoming and transmitted rays.

What to notice

Both angles are measured from the normal, not from the surface.

Why it matters

Most sign and direction mistakes come from measuring the angle from the wrong reference line.

Control: Incident angleGraph: Incident to refracted angleGraph: Bend relative to the normalEquation

θ_{1}

Challenge mode

Use the real ray diagram, not a separate puzzle state. The checks read the live angles, indices, and overlays from the same boundary you are editing.

0/2 solved

MatchStretch

0 of 5 checks

Compare a denser variant

Open compare mode from Air to glass. Leave Setup A near the baseline, then edit Setup B so the lower medium is noticeably denser and the incident angle is steeper.

Compare modeGraph-linkedGuided start2 hints

Suggested start

Keep A as the baseline while you edit B.

Pending

Open the bend graph.

Incident to refracted angle

Pending

Edit Setup B while compare mode is active.

Explore

Pending

Keep Setup A near the air-to-glass baseline.

Pending

Make Setup B use a denser lower medium.

Pending

Make Setup B use a steeper incident angle.

The checklist updates from the live simulation state, active graph, overlays, inspect time, and compare setup.

Light crosses from n1 = 1 to n2 = 1.5 at 50°. The ray refracts to 30.71°, bends toward the normal, and the relative speed changes by v2/v1 = 0.67.

Equation detailsDeeper interpretation, notes, and worked variable context.

Snell's law

Relates the incident and transmitted angles to the refractive indices on each side of the boundary.

n_{1} sin (θ_{1}) = n_{2} sin (θ_{2})

θ_{1}

Incident angle 50°

n_{1}

Top-medium index 1

n_{2}

Bottom-medium index 1.5

Index and speed

A larger refractive index means a lower light speed in that medium.

n = \frac{c}{v}

n_{1}

Top-medium index 1

n_{2}

Bottom-medium index 1.5

Critical angle

When light tries to go from higher n to lower n, this angle marks the limit where the transmitted ray would flatten along the boundary.

sin (θ_{c}) = \frac{n _{2}}{n _{1}} (n_{1} > n_{2})

Beyond this limit there is no real transmitted angle, which is the entry point to total internal reflection.

θ_{1}

Incident angle 50°

n_{1}

Top-medium index 1

n_{2}

Bottom-medium index 1.5

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. Challenge mode has 2 compact tasks ready. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

Short explanation

What the system is doing

Refraction is a boundary story. Light reaches an interface, the wave speed changes because the refractive index changes, and the ray direction shifts just enough to keep the boundary geometry consistent on both sides.

This concept keeps one compact boundary-and-ray picture in charge. Incident angle, refractive indices, speed ratio, graph previews, prediction mode, compare mode, and the worked examples all read from the same interface state so the direction change never drifts away from Snell's law.

Key ideas

01A larger refractive index means a lower wave speed in that medium, so entering the higher-index side bends the ray toward the normal.

02Snell's law, n_1 sin(theta_1) = n_2 sin(theta_2), connects the two boundary angles quantitatively rather than by a memorized picture alone.

03At normal incidence the speed can still change while the direction does not, and when light tries to go from higher n to lower n too steeply there is no real transmitted angle.

Live worked example

Solve the exact state on screen.

Solve the current boundary, not a detached worksheet. The substitutions track the live incident angle and refractive indices, and the same values stay visible on the ray diagram and graphs.

Live valuesFollowing current parameters

For the current interface, what transmitted angle follows from Snell's law?

θ_{1}

Incident angle

50 °

n_{1}

Top-medium index

n_{2}

Bottom-medium index

1.5

1. Start from Snell's law

Use

n_{1} sin (θ_{1}) = n_{2} sin (θ_{2})

2. Rearrange for the transmitted sine

sin (θ_{2}) = \frac{n _{1}}{n _{2}} sin (θ_{1}) = \frac{1}{1.5} sin (5 0^{\circ}) = 0.51

3. Interpret the result

θ_{2} = sin^{- 1} (0.51) = 30.7 1^{\circ}

Transmitted result

θ_{2} = 30.7 1^{\circ}

The lower medium is slower, so the transmitted angle is smaller and the ray bends toward the normal.

Common misconception

The boundary bends the ray because it gives the light a sideways push at the interface.

The directional change comes from the speed difference between the two media, not from a separate sideways force at the boundary.

That is why the same boundary can change the speed without changing the direction at normal incidence, and why a bigger index contrast changes the bend even when the interface itself stays fixed.

Mini challenge

A ray goes from air into glass at the same incident angle you see now. Before you adjust anything, what should happen to the transmitted ray?

Prediction prompt

Decide whether the ray should move closer to the normal or farther away, and whether the speed should rise or fall.

Check your reasoning

It should slow down and bend toward the normal.

A larger refractive index means a smaller speed. Snell's law then requires the transmitted angle to shrink relative to the normal, so the ray bends inward rather than outward.

Quick test

Variable effect

Question 1 of 4

Use the speed story, the angle story, and the graph story together. The goal is to reason from the live boundary, not to quote a slogan.

What happens when light crosses from a lower-index medium into a higher-index medium at the same incident angle?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

The simulation shows a horizontal boundary separating a top medium from a bottom medium, with a dashed normal line through the point where the ray hits the interface. One incoming ray approaches from the upper left, and the transmitted ray leaves into the lower right unless the current setup exceeds the critical-angle limit.

Optional overlays show the angle markers, the medium-speed guide, and the critical-angle threshold used to introduce total internal reflection honestly.

Graph summary

The first graph plots refracted angle against incident angle for the current media pair, so hovering it previews a different boundary setup rather than a later moment in time.

The second graph plots the signed bend relative to the normal, with positive values meaning toward the normal and negative values meaning away. When a critical angle exists, the plotted branch stops where no real transmitted angle remains.

Keep moving through the concept map.

These suggestions come from the concept registry, so the reason label reflects either curated guidance or the fallback progression logic.

Color-dependent bendingOptics

Refraction / Snell's Law

See each variable before you move it.

Normal and angle guide

Compare a denser variant

What the system is doing

Solve the exact state on screen.

For the current interface, what transmitted angle follows from Snell's law?

What happens when light crosses from a lower-index medium into a higher-index medium at the same incident angle?

Keep moving through the concept map.

Dispersion / Refractive Index and Color

Total Internal Reflection

Diffraction